Deconvolution of astronomical images using SOR with adaptive relaxation

Area of Science:

• Astronomy and Astrophysics
• Image Processing
• Computational Science

Background:

• Astronomical images are often degraded by atmospheric turbulence, necessitating advanced deconvolution techniques.
• Iterative methods like Successive Over-Relaxation (SOR) show promise for image restoration but require careful parameter selection.
• Choosing the optimal relaxation parameter for SOR has historically relied on empirical experimentation.

Purpose of the Study:

• To develop and evaluate a novel strategy for selecting and updating the relaxation parameter in SOR algorithms for image deconvolution.
• To enhance the performance of SOR and its positivity-constrained variant (+SOR) for astronomical image restoration.
• To extend the SOR approach to blind deconvolution problems.

Main Methods:

• A constructive strategy for choosing and updating the relaxation parameter in SOR and +SOR algorithms was developed.
• The proposed method was applied to astronomical image deconvolution, including restoration of turbulence-distorted images.
• The algorithm was extended to address blind deconvolution, recovering both the object and point-spread function.
• Numerical inversions were performed using artificial and real astronomical data.

Main Results:

• The proposed +SOR algorithm consistently yielded the highest quality results compared to conjugate gradient methods.
• +SOR demonstrated effectiveness in detecting small object changes between frames, crucial for multi-frame blind deconvolution.
• The new strategy for parameter selection optimized SOR performance at finite iteration counts.

Conclusions:

• The developed strategy for relaxation parameter optimization significantly enhances the performance of SOR-based image deconvolution.
• +SOR offers a superior approach for restoring degraded astronomical images and addressing blind deconvolution challenges.
• The method's ability to detect object variations makes it valuable for advanced multi-frame analyses.